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A straight line drawn from the point P(1,3, 2), parallel to the line \(\frac{x-2}{1}=\frac{y-4}{2}=\frac{z-6}{1}\), intersects the plane L1 : x - y + 3z = 6 at the point Q. Another straight line which passes through Q and is perpendicular to the plane L1 intersects the plane L2 : 2x - y + z = -4 at the point R. Then which of the following statements is (are) TRUE ?
A straight line drawn from the point P(1,3, 2), parallel to the line \(\frac{x-2}{1}=\frac{y-4}{2}=\frac{z-6}{1}\), intersects the plane L1 : x - y + 3z = 6 at the point Q. Another straight line which passes through Q and is perpendicular to the plane L1 intersects the plane L2 : 2x - y + z = -4 at the point R. Then which of the following statements is (are) TRUE ?
Updated On: Jun 10, 2024
- The length of the line segment PQ is \(\sqrt6\)
- The coordinates of R are (1, 6, 3)
- The centroid of the triangle PQR is \((\frac{4}{3},\frac{14}{3},\frac{5}{3})\)
- The perimeter of the triangle PQR is \(\sqrt2+\sqrt6+\sqrt{11}\)
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The Correct Option is A, C
Solution and Explanation
The correct option is (A): The length of the line segment PQ is \(\sqrt6\) and (C): The centroid of the triangle PQR is \((\frac{4}{3},\frac{14}{3},\frac{5}{3})\).
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